Semiclassical second order vibrational perturbation theory for hopping rates of H and D atoms on Pt(111) and H on Ru(0001)

Abstract

Wolynes's theory for tunneling in dissipative systems was constructed for parabolic barriers. Its recent generalization to anharmonic potentials is further developed, most notably by employing the second order vibrational perturbation theory expression for the action, derived by Miller and coworkers. With this construct there is no need to know the full potential energy surface involved in the hopping, it is sufficient to know well and barrier frequencies, barrier heights, friction coefficients and the fourth order derivative of the potential at the barrier top. The resulting theory is applied to model the experimentally measured hopping rates of H and D atoms on a Pt(111) surface and H atom hopping over a barrier on the Ru(0001) surface. In all cases, the results indicate that the barrier frequency is substantially larger than the well frequency. The comparison with experiment sheds light on the information content of the measured data.